Properties

Label 128.3.h.a.111.3
Level $128$
Weight $3$
Character 128.111
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 111.3
Character \(\chi\) \(=\) 128.111
Dual form 128.3.h.a.15.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.58190 - 0.655246i) q^{3} +(4.18866 - 1.73500i) q^{5} +(-3.93197 - 3.93197i) q^{7} +(-4.29089 - 4.29089i) q^{9} +O(q^{10})\) \(q+(-1.58190 - 0.655246i) q^{3} +(4.18866 - 1.73500i) q^{5} +(-3.93197 - 3.93197i) q^{7} +(-4.29089 - 4.29089i) q^{9} +(14.2355 - 5.89652i) q^{11} +(0.454935 + 0.188440i) q^{13} -7.76291 q^{15} -26.5635i q^{17} +(7.25040 - 17.5040i) q^{19} +(3.64359 + 8.79641i) q^{21} +(-0.775848 + 0.775848i) q^{23} +(-3.14303 + 3.14303i) q^{25} +(9.87340 + 23.8365i) q^{27} +(-17.9907 + 43.4334i) q^{29} +39.6852i q^{31} -26.3828 q^{33} +(-23.2916 - 9.64771i) q^{35} +(36.4715 - 15.1070i) q^{37} +(-0.596189 - 0.596189i) q^{39} +(38.9661 + 38.9661i) q^{41} +(14.2899 - 5.91907i) q^{43} +(-25.4177 - 10.5284i) q^{45} -62.1759 q^{47} -18.0792i q^{49} +(-17.4057 + 42.0210i) q^{51} +(11.4986 + 27.7600i) q^{53} +(49.3970 - 49.3970i) q^{55} +(-22.9389 + 22.9389i) q^{57} +(5.30584 + 12.8094i) q^{59} +(14.1407 - 34.1386i) q^{61} +33.7433i q^{63} +2.23251 q^{65} +(-26.1257 - 10.8216i) q^{67} +(1.73569 - 0.718946i) q^{69} +(-17.7859 - 17.7859i) q^{71} +(12.8313 + 12.8313i) q^{73} +(7.03144 - 2.91252i) q^{75} +(-79.1584 - 32.7885i) q^{77} +144.157 q^{79} +10.4375i q^{81} +(10.9897 - 26.5314i) q^{83} +(-46.0877 - 111.266i) q^{85} +(56.9192 - 56.9192i) q^{87} +(-5.92267 + 5.92267i) q^{89} +(-1.04785 - 2.52973i) q^{91} +(26.0036 - 62.7782i) q^{93} -85.8978i q^{95} +66.9192 q^{97} +(-86.3841 - 35.7815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.58190 0.655246i −0.527302 0.218415i 0.103119 0.994669i \(-0.467118\pi\)
−0.630421 + 0.776254i \(0.717118\pi\)
\(4\) 0 0
\(5\) 4.18866 1.73500i 0.837732 0.347000i 0.0777729 0.996971i \(-0.475219\pi\)
0.759959 + 0.649971i \(0.225219\pi\)
\(6\) 0 0
\(7\) −3.93197 3.93197i −0.561710 0.561710i 0.368083 0.929793i \(-0.380014\pi\)
−0.929793 + 0.368083i \(0.880014\pi\)
\(8\) 0 0
\(9\) −4.29089 4.29089i −0.476765 0.476765i
\(10\) 0 0
\(11\) 14.2355 5.89652i 1.29413 0.536048i 0.373919 0.927462i \(-0.378014\pi\)
0.920215 + 0.391414i \(0.128014\pi\)
\(12\) 0 0
\(13\) 0.454935 + 0.188440i 0.0349950 + 0.0144954i 0.400112 0.916466i \(-0.368971\pi\)
−0.365117 + 0.930962i \(0.618971\pi\)
\(14\) 0 0
\(15\) −7.76291 −0.517527
\(16\) 0 0
\(17\) 26.5635i 1.56256i −0.624181 0.781280i \(-0.714567\pi\)
0.624181 0.781280i \(-0.285433\pi\)
\(18\) 0 0
\(19\) 7.25040 17.5040i 0.381600 0.921264i −0.610057 0.792358i \(-0.708853\pi\)
0.991657 0.128906i \(-0.0411466\pi\)
\(20\) 0 0
\(21\) 3.64359 + 8.79641i 0.173504 + 0.418877i
\(22\) 0 0
\(23\) −0.775848 + 0.775848i −0.0337325 + 0.0337325i −0.723772 0.690039i \(-0.757593\pi\)
0.690039 + 0.723772i \(0.257593\pi\)
\(24\) 0 0
\(25\) −3.14303 + 3.14303i −0.125721 + 0.125721i
\(26\) 0 0
\(27\) 9.87340 + 23.8365i 0.365682 + 0.882833i
\(28\) 0 0
\(29\) −17.9907 + 43.4334i −0.620369 + 1.49770i 0.230901 + 0.972977i \(0.425833\pi\)
−0.851271 + 0.524727i \(0.824167\pi\)
\(30\) 0 0
\(31\) 39.6852i 1.28017i 0.768306 + 0.640083i \(0.221100\pi\)
−0.768306 + 0.640083i \(0.778900\pi\)
\(32\) 0 0
\(33\) −26.3828 −0.799480
\(34\) 0 0
\(35\) −23.2916 9.64771i −0.665475 0.275649i
\(36\) 0 0
\(37\) 36.4715 15.1070i 0.985717 0.408297i 0.169177 0.985586i \(-0.445889\pi\)
0.816540 + 0.577288i \(0.195889\pi\)
\(38\) 0 0
\(39\) −0.596189 0.596189i −0.0152869 0.0152869i
\(40\) 0 0
\(41\) 38.9661 + 38.9661i 0.950392 + 0.950392i 0.998826 0.0484342i \(-0.0154231\pi\)
−0.0484342 + 0.998826i \(0.515423\pi\)
\(42\) 0 0
\(43\) 14.2899 5.91907i 0.332324 0.137653i −0.210282 0.977641i \(-0.567438\pi\)
0.542605 + 0.839988i \(0.317438\pi\)
\(44\) 0 0
\(45\) −25.4177 10.5284i −0.564839 0.233964i
\(46\) 0 0
\(47\) −62.1759 −1.32289 −0.661446 0.749993i \(-0.730057\pi\)
−0.661446 + 0.749993i \(0.730057\pi\)
\(48\) 0 0
\(49\) 18.0792i 0.368964i
\(50\) 0 0
\(51\) −17.4057 + 42.0210i −0.341287 + 0.823940i
\(52\) 0 0
\(53\) 11.4986 + 27.7600i 0.216954 + 0.523773i 0.994462 0.105100i \(-0.0335163\pi\)
−0.777508 + 0.628874i \(0.783516\pi\)
\(54\) 0 0
\(55\) 49.3970 49.3970i 0.898128 0.898128i
\(56\) 0 0
\(57\) −22.9389 + 22.9389i −0.402437 + 0.402437i
\(58\) 0 0
\(59\) 5.30584 + 12.8094i 0.0899295 + 0.217109i 0.962445 0.271478i \(-0.0875124\pi\)
−0.872515 + 0.488587i \(0.837512\pi\)
\(60\) 0 0
\(61\) 14.1407 34.1386i 0.231814 0.559650i −0.764576 0.644533i \(-0.777052\pi\)
0.996391 + 0.0848835i \(0.0270518\pi\)
\(62\) 0 0
\(63\) 33.7433i 0.535607i
\(64\) 0 0
\(65\) 2.23251 0.0343463
\(66\) 0 0
\(67\) −26.1257 10.8216i −0.389937 0.161517i 0.179097 0.983831i \(-0.442682\pi\)
−0.569033 + 0.822314i \(0.692682\pi\)
\(68\) 0 0
\(69\) 1.73569 0.718946i 0.0251549 0.0104195i
\(70\) 0 0
\(71\) −17.7859 17.7859i −0.250505 0.250505i 0.570672 0.821178i \(-0.306683\pi\)
−0.821178 + 0.570672i \(0.806683\pi\)
\(72\) 0 0
\(73\) 12.8313 + 12.8313i 0.175771 + 0.175771i 0.789510 0.613738i \(-0.210335\pi\)
−0.613738 + 0.789510i \(0.710335\pi\)
\(74\) 0 0
\(75\) 7.03144 2.91252i 0.0937525 0.0388336i
\(76\) 0 0
\(77\) −79.1584 32.7885i −1.02803 0.425824i
\(78\) 0 0
\(79\) 144.157 1.82477 0.912383 0.409337i \(-0.134240\pi\)
0.912383 + 0.409337i \(0.134240\pi\)
\(80\) 0 0
\(81\) 10.4375i 0.128858i
\(82\) 0 0
\(83\) 10.9897 26.5314i 0.132406 0.319655i −0.843747 0.536741i \(-0.819655\pi\)
0.976153 + 0.217086i \(0.0696552\pi\)
\(84\) 0 0
\(85\) −46.0877 111.266i −0.542208 1.30901i
\(86\) 0 0
\(87\) 56.9192 56.9192i 0.654244 0.654244i
\(88\) 0 0
\(89\) −5.92267 + 5.92267i −0.0665469 + 0.0665469i −0.739597 0.673050i \(-0.764984\pi\)
0.673050 + 0.739597i \(0.264984\pi\)
\(90\) 0 0
\(91\) −1.04785 2.52973i −0.0115148 0.0277993i
\(92\) 0 0
\(93\) 26.0036 62.7782i 0.279608 0.675034i
\(94\) 0 0
\(95\) 85.8978i 0.904187i
\(96\) 0 0
\(97\) 66.9192 0.689889 0.344944 0.938623i \(-0.387898\pi\)
0.344944 + 0.938623i \(0.387898\pi\)
\(98\) 0 0
\(99\) −86.3841 35.7815i −0.872566 0.361429i
\(100\) 0 0
\(101\) 23.3697 9.68007i 0.231384 0.0958422i −0.263979 0.964528i \(-0.585035\pi\)
0.495363 + 0.868686i \(0.335035\pi\)
\(102\) 0 0
\(103\) 15.5454 + 15.5454i 0.150927 + 0.150927i 0.778532 0.627605i \(-0.215965\pi\)
−0.627605 + 0.778532i \(0.715965\pi\)
\(104\) 0 0
\(105\) 30.5235 + 30.5235i 0.290700 + 0.290700i
\(106\) 0 0
\(107\) −107.060 + 44.3456i −1.00056 + 0.414444i −0.822001 0.569485i \(-0.807143\pi\)
−0.178556 + 0.983930i \(0.557143\pi\)
\(108\) 0 0
\(109\) 82.3132 + 34.0952i 0.755167 + 0.312800i 0.726848 0.686799i \(-0.240985\pi\)
0.0283190 + 0.999599i \(0.490985\pi\)
\(110\) 0 0
\(111\) −67.5933 −0.608949
\(112\) 0 0
\(113\) 9.91566i 0.0877492i 0.999037 + 0.0438746i \(0.0139702\pi\)
−0.999037 + 0.0438746i \(0.986030\pi\)
\(114\) 0 0
\(115\) −1.90367 + 4.59586i −0.0165536 + 0.0399640i
\(116\) 0 0
\(117\) −1.14350 2.76065i −0.00977350 0.0235953i
\(118\) 0 0
\(119\) −104.447 + 104.447i −0.877705 + 0.877705i
\(120\) 0 0
\(121\) 82.3196 82.3196i 0.680327 0.680327i
\(122\) 0 0
\(123\) −36.1082 87.1730i −0.293563 0.708724i
\(124\) 0 0
\(125\) −51.0869 + 123.335i −0.408695 + 0.986678i
\(126\) 0 0
\(127\) 59.4093i 0.467790i −0.972262 0.233895i \(-0.924853\pi\)
0.972262 0.233895i \(-0.0751471\pi\)
\(128\) 0 0
\(129\) −26.4837 −0.205300
\(130\) 0 0
\(131\) 176.426 + 73.0781i 1.34676 + 0.557848i 0.935390 0.353618i \(-0.115049\pi\)
0.411375 + 0.911466i \(0.365049\pi\)
\(132\) 0 0
\(133\) −97.3336 + 40.3169i −0.731832 + 0.303135i
\(134\) 0 0
\(135\) 82.7126 + 82.7126i 0.612686 + 0.612686i
\(136\) 0 0
\(137\) −138.710 138.710i −1.01248 1.01248i −0.999921 0.0125608i \(-0.996002\pi\)
−0.0125608 0.999921i \(-0.503998\pi\)
\(138\) 0 0
\(139\) 63.7662 26.4128i 0.458750 0.190020i −0.141327 0.989963i \(-0.545137\pi\)
0.600077 + 0.799943i \(0.295137\pi\)
\(140\) 0 0
\(141\) 98.3563 + 40.7405i 0.697563 + 0.288940i
\(142\) 0 0
\(143\) 7.58736 0.0530584
\(144\) 0 0
\(145\) 213.142i 1.46994i
\(146\) 0 0
\(147\) −11.8464 + 28.5996i −0.0805874 + 0.194555i
\(148\) 0 0
\(149\) 41.3888 + 99.9214i 0.277777 + 0.670613i 0.999773 0.0212835i \(-0.00677526\pi\)
−0.721996 + 0.691897i \(0.756775\pi\)
\(150\) 0 0
\(151\) −159.036 + 159.036i −1.05322 + 1.05322i −0.0547164 + 0.998502i \(0.517425\pi\)
−0.998502 + 0.0547164i \(0.982575\pi\)
\(152\) 0 0
\(153\) −113.981 + 113.981i −0.744974 + 0.744974i
\(154\) 0 0
\(155\) 68.8537 + 166.228i 0.444218 + 1.07244i
\(156\) 0 0
\(157\) 31.5775 76.2349i 0.201131 0.485573i −0.790843 0.612020i \(-0.790357\pi\)
0.991973 + 0.126447i \(0.0403573\pi\)
\(158\) 0 0
\(159\) 51.4480i 0.323573i
\(160\) 0 0
\(161\) 6.10122 0.0378958
\(162\) 0 0
\(163\) 192.658 + 79.8016i 1.18195 + 0.489581i 0.885126 0.465351i \(-0.154072\pi\)
0.296826 + 0.954932i \(0.404072\pi\)
\(164\) 0 0
\(165\) −110.509 + 45.7742i −0.669749 + 0.277419i
\(166\) 0 0
\(167\) −76.7432 76.7432i −0.459540 0.459540i 0.438964 0.898504i \(-0.355345\pi\)
−0.898504 + 0.438964i \(0.855345\pi\)
\(168\) 0 0
\(169\) −119.330 119.330i −0.706092 0.706092i
\(170\) 0 0
\(171\) −106.218 + 43.9971i −0.621160 + 0.257293i
\(172\) 0 0
\(173\) 46.0052 + 19.0560i 0.265926 + 0.110150i 0.511663 0.859187i \(-0.329030\pi\)
−0.245737 + 0.969337i \(0.579030\pi\)
\(174\) 0 0
\(175\) 24.7166 0.141238
\(176\) 0 0
\(177\) 23.7399i 0.134124i
\(178\) 0 0
\(179\) 29.4799 71.1707i 0.164692 0.397602i −0.819891 0.572520i \(-0.805966\pi\)
0.984583 + 0.174918i \(0.0559660\pi\)
\(180\) 0 0
\(181\) 46.7381 + 112.836i 0.258222 + 0.623402i 0.998821 0.0485445i \(-0.0154583\pi\)
−0.740599 + 0.671947i \(0.765458\pi\)
\(182\) 0 0
\(183\) −44.7384 + 44.7384i −0.244472 + 0.244472i
\(184\) 0 0
\(185\) 126.556 126.556i 0.684087 0.684087i
\(186\) 0 0
\(187\) −156.632 378.144i −0.837606 2.02216i
\(188\) 0 0
\(189\) 54.9025 132.546i 0.290489 0.701303i
\(190\) 0 0
\(191\) 227.376i 1.19045i 0.803559 + 0.595226i \(0.202937\pi\)
−0.803559 + 0.595226i \(0.797063\pi\)
\(192\) 0 0
\(193\) −46.4565 −0.240707 −0.120354 0.992731i \(-0.538403\pi\)
−0.120354 + 0.992731i \(0.538403\pi\)
\(194\) 0 0
\(195\) −3.53162 1.46285i −0.0181109 0.00750177i
\(196\) 0 0
\(197\) −186.490 + 77.2467i −0.946650 + 0.392115i −0.801971 0.597363i \(-0.796215\pi\)
−0.144680 + 0.989479i \(0.546215\pi\)
\(198\) 0 0
\(199\) −54.5057 54.5057i −0.273898 0.273898i 0.556769 0.830667i \(-0.312041\pi\)
−0.830667 + 0.556769i \(0.812041\pi\)
\(200\) 0 0
\(201\) 34.2376 + 34.2376i 0.170336 + 0.170336i
\(202\) 0 0
\(203\) 241.518 100.040i 1.18974 0.492808i
\(204\) 0 0
\(205\) 230.822 + 95.6095i 1.12596 + 0.466388i
\(206\) 0 0
\(207\) 6.65815 0.0321650
\(208\) 0 0
\(209\) 291.930i 1.39679i
\(210\) 0 0
\(211\) −35.0586 + 84.6390i −0.166155 + 0.401133i −0.984923 0.172991i \(-0.944657\pi\)
0.818769 + 0.574123i \(0.194657\pi\)
\(212\) 0 0
\(213\) 16.4814 + 39.7897i 0.0773776 + 0.186806i
\(214\) 0 0
\(215\) 49.5860 49.5860i 0.230632 0.230632i
\(216\) 0 0
\(217\) 156.041 156.041i 0.719082 0.719082i
\(218\) 0 0
\(219\) −11.8902 28.7056i −0.0542933 0.131076i
\(220\) 0 0
\(221\) 5.00564 12.0847i 0.0226499 0.0546818i
\(222\) 0 0
\(223\) 428.136i 1.91989i −0.280181 0.959947i \(-0.590394\pi\)
0.280181 0.959947i \(-0.409606\pi\)
\(224\) 0 0
\(225\) 26.9728 0.119879
\(226\) 0 0
\(227\) 112.195 + 46.4728i 0.494252 + 0.204726i 0.615865 0.787852i \(-0.288807\pi\)
−0.121613 + 0.992578i \(0.538807\pi\)
\(228\) 0 0
\(229\) 128.033 53.0331i 0.559097 0.231586i −0.0851960 0.996364i \(-0.527152\pi\)
0.644293 + 0.764779i \(0.277152\pi\)
\(230\) 0 0
\(231\) 103.736 + 103.736i 0.449076 + 0.449076i
\(232\) 0 0
\(233\) −90.6042 90.6042i −0.388859 0.388859i 0.485421 0.874280i \(-0.338666\pi\)
−0.874280 + 0.485421i \(0.838666\pi\)
\(234\) 0 0
\(235\) −260.434 + 107.875i −1.10823 + 0.459043i
\(236\) 0 0
\(237\) −228.042 94.4581i −0.962202 0.398557i
\(238\) 0 0
\(239\) −283.775 −1.18734 −0.593672 0.804707i \(-0.702323\pi\)
−0.593672 + 0.804707i \(0.702323\pi\)
\(240\) 0 0
\(241\) 309.483i 1.28416i 0.766636 + 0.642082i \(0.221929\pi\)
−0.766636 + 0.642082i \(0.778071\pi\)
\(242\) 0 0
\(243\) 95.6997 231.040i 0.393826 0.950780i
\(244\) 0 0
\(245\) −31.3674 75.7277i −0.128030 0.309093i
\(246\) 0 0
\(247\) 6.59693 6.59693i 0.0267082 0.0267082i
\(248\) 0 0
\(249\) −34.7692 + 34.7692i −0.139635 + 0.139635i
\(250\) 0 0
\(251\) 33.9351 + 81.9265i 0.135199 + 0.326400i 0.976951 0.213465i \(-0.0684750\pi\)
−0.841751 + 0.539866i \(0.818475\pi\)
\(252\) 0 0
\(253\) −6.46975 + 15.6194i −0.0255721 + 0.0617366i
\(254\) 0 0
\(255\) 206.210i 0.808668i
\(256\) 0 0
\(257\) 193.069 0.751241 0.375621 0.926774i \(-0.377430\pi\)
0.375621 + 0.926774i \(0.377430\pi\)
\(258\) 0 0
\(259\) −202.805 84.0047i −0.783032 0.324342i
\(260\) 0 0
\(261\) 263.564 109.172i 1.00982 0.418283i
\(262\) 0 0
\(263\) 14.4799 + 14.4799i 0.0550568 + 0.0550568i 0.734099 0.679042i \(-0.237605\pi\)
−0.679042 + 0.734099i \(0.737605\pi\)
\(264\) 0 0
\(265\) 96.3271 + 96.3271i 0.363498 + 0.363498i
\(266\) 0 0
\(267\) 13.2499 5.48830i 0.0496252 0.0205554i
\(268\) 0 0
\(269\) −125.951 52.1707i −0.468220 0.193943i 0.136083 0.990697i \(-0.456549\pi\)
−0.604303 + 0.796754i \(0.706549\pi\)
\(270\) 0 0
\(271\) 490.650 1.81052 0.905258 0.424863i \(-0.139678\pi\)
0.905258 + 0.424863i \(0.139678\pi\)
\(272\) 0 0
\(273\) 4.68840i 0.0171736i
\(274\) 0 0
\(275\) −26.2096 + 63.2755i −0.0953076 + 0.230093i
\(276\) 0 0
\(277\) −183.667 443.412i −0.663059 1.60076i −0.792985 0.609241i \(-0.791474\pi\)
0.129926 0.991524i \(-0.458526\pi\)
\(278\) 0 0
\(279\) 170.285 170.285i 0.610339 0.610339i
\(280\) 0 0
\(281\) −164.474 + 164.474i −0.585316 + 0.585316i −0.936359 0.351043i \(-0.885827\pi\)
0.351043 + 0.936359i \(0.385827\pi\)
\(282\) 0 0
\(283\) 98.6436 + 238.147i 0.348564 + 0.841508i 0.996790 + 0.0800601i \(0.0255112\pi\)
−0.648226 + 0.761448i \(0.724489\pi\)
\(284\) 0 0
\(285\) −56.2842 + 135.882i −0.197488 + 0.476779i
\(286\) 0 0
\(287\) 306.427i 1.06769i
\(288\) 0 0
\(289\) −416.621 −1.44159
\(290\) 0 0
\(291\) −105.860 43.8486i −0.363779 0.150682i
\(292\) 0 0
\(293\) −60.5536 + 25.0821i −0.206668 + 0.0856045i −0.483616 0.875280i \(-0.660677\pi\)
0.276948 + 0.960885i \(0.410677\pi\)
\(294\) 0 0
\(295\) 44.4487 + 44.4487i 0.150674 + 0.150674i
\(296\) 0 0
\(297\) 281.105 + 281.105i 0.946481 + 0.946481i
\(298\) 0 0
\(299\) −0.499162 + 0.206759i −0.00166944 + 0.000691503i
\(300\) 0 0
\(301\) −79.4611 32.9139i −0.263990 0.109348i
\(302\) 0 0
\(303\) −43.3115 −0.142942
\(304\) 0 0
\(305\) 167.529i 0.549276i
\(306\) 0 0
\(307\) −166.166 + 401.160i −0.541257 + 1.30671i 0.382580 + 0.923923i \(0.375036\pi\)
−0.923836 + 0.382787i \(0.874964\pi\)
\(308\) 0 0
\(309\) −14.4053 34.7775i −0.0466191 0.112548i
\(310\) 0 0
\(311\) 261.640 261.640i 0.841288 0.841288i −0.147739 0.989026i \(-0.547199\pi\)
0.989026 + 0.147739i \(0.0471995\pi\)
\(312\) 0 0
\(313\) −301.723 + 301.723i −0.963972 + 0.963972i −0.999373 0.0354015i \(-0.988729\pi\)
0.0354015 + 0.999373i \(0.488729\pi\)
\(314\) 0 0
\(315\) 58.5445 + 141.339i 0.185856 + 0.448695i
\(316\) 0 0
\(317\) 11.4511 27.6454i 0.0361233 0.0872094i −0.904788 0.425862i \(-0.859971\pi\)
0.940912 + 0.338652i \(0.109971\pi\)
\(318\) 0 0
\(319\) 724.378i 2.27078i
\(320\) 0 0
\(321\) 198.415 0.618117
\(322\) 0 0
\(323\) −464.968 192.596i −1.43953 0.596273i
\(324\) 0 0
\(325\) −2.02215 + 0.837602i −0.00622200 + 0.00257724i
\(326\) 0 0
\(327\) −107.871 107.871i −0.329880 0.329880i
\(328\) 0 0
\(329\) 244.474 + 244.474i 0.743081 + 0.743081i
\(330\) 0 0
\(331\) 117.333 48.6009i 0.354480 0.146830i −0.198335 0.980134i \(-0.563553\pi\)
0.552815 + 0.833304i \(0.313553\pi\)
\(332\) 0 0
\(333\) −221.318 91.6728i −0.664617 0.275294i
\(334\) 0 0
\(335\) −128.207 −0.382709
\(336\) 0 0
\(337\) 148.325i 0.440134i 0.975485 + 0.220067i \(0.0706276\pi\)
−0.975485 + 0.220067i \(0.929372\pi\)
\(338\) 0 0
\(339\) 6.49720 15.6856i 0.0191658 0.0462703i
\(340\) 0 0
\(341\) 234.004 + 564.937i 0.686230 + 1.65671i
\(342\) 0 0
\(343\) −263.753 + 263.753i −0.768961 + 0.768961i
\(344\) 0 0
\(345\) 6.02284 6.02284i 0.0174575 0.0174575i
\(346\) 0 0
\(347\) 215.625 + 520.565i 0.621398 + 1.50019i 0.850062 + 0.526682i \(0.176564\pi\)
−0.228664 + 0.973505i \(0.573436\pi\)
\(348\) 0 0
\(349\) −92.9006 + 224.282i −0.266191 + 0.642641i −0.999298 0.0374720i \(-0.988070\pi\)
0.733107 + 0.680113i \(0.238070\pi\)
\(350\) 0 0
\(351\) 12.7046i 0.0361955i
\(352\) 0 0
\(353\) 453.234 1.28395 0.641975 0.766726i \(-0.278115\pi\)
0.641975 + 0.766726i \(0.278115\pi\)
\(354\) 0 0
\(355\) −105.357 43.6405i −0.296782 0.122931i
\(356\) 0 0
\(357\) 233.664 96.7866i 0.654520 0.271111i
\(358\) 0 0
\(359\) −175.857 175.857i −0.489852 0.489852i 0.418407 0.908259i \(-0.362588\pi\)
−0.908259 + 0.418407i \(0.862588\pi\)
\(360\) 0 0
\(361\) 1.44333 + 1.44333i 0.00399816 + 0.00399816i
\(362\) 0 0
\(363\) −184.161 + 76.2821i −0.507332 + 0.210144i
\(364\) 0 0
\(365\) 76.0082 + 31.4836i 0.208242 + 0.0862566i
\(366\) 0 0
\(367\) −115.194 −0.313879 −0.156939 0.987608i \(-0.550163\pi\)
−0.156939 + 0.987608i \(0.550163\pi\)
\(368\) 0 0
\(369\) 334.398i 0.906228i
\(370\) 0 0
\(371\) 63.9394 154.363i 0.172343 0.416074i
\(372\) 0 0
\(373\) −95.1961 229.824i −0.255217 0.616149i 0.743393 0.668855i \(-0.233215\pi\)
−0.998610 + 0.0527059i \(0.983215\pi\)
\(374\) 0 0
\(375\) 161.629 161.629i 0.431011 0.431011i
\(376\) 0 0
\(377\) −16.3692 + 16.3692i −0.0434197 + 0.0434197i
\(378\) 0 0
\(379\) −264.738 639.134i −0.698517 1.68637i −0.726873 0.686772i \(-0.759027\pi\)
0.0283560 0.999598i \(-0.490973\pi\)
\(380\) 0 0
\(381\) −38.9277 + 93.9798i −0.102172 + 0.246666i
\(382\) 0 0
\(383\) 217.725i 0.568473i 0.958754 + 0.284236i \(0.0917401\pi\)
−0.958754 + 0.284236i \(0.908260\pi\)
\(384\) 0 0
\(385\) −388.455 −1.00897
\(386\) 0 0
\(387\) −86.7145 35.9183i −0.224068 0.0928122i
\(388\) 0 0
\(389\) 452.405 187.392i 1.16299 0.481728i 0.284123 0.958788i \(-0.408297\pi\)
0.878871 + 0.477060i \(0.158297\pi\)
\(390\) 0 0
\(391\) 20.6092 + 20.6092i 0.0527091 + 0.0527091i
\(392\) 0 0
\(393\) −231.205 231.205i −0.588308 0.588308i
\(394\) 0 0
\(395\) 603.823 250.112i 1.52866 0.633194i
\(396\) 0 0
\(397\) −281.846 116.745i −0.709940 0.294067i −0.00166042 0.999999i \(-0.500529\pi\)
−0.708280 + 0.705932i \(0.750529\pi\)
\(398\) 0 0
\(399\) 180.390 0.452105
\(400\) 0 0
\(401\) 173.814i 0.433452i −0.976232 0.216726i \(-0.930462\pi\)
0.976232 0.216726i \(-0.0695378\pi\)
\(402\) 0 0
\(403\) −7.47829 + 18.0542i −0.0185565 + 0.0447995i
\(404\) 0 0
\(405\) 18.1090 + 43.7190i 0.0447136 + 0.107948i
\(406\) 0 0
\(407\) 430.110 430.110i 1.05678 1.05678i
\(408\) 0 0
\(409\) 322.065 322.065i 0.787446 0.787446i −0.193629 0.981075i \(-0.562026\pi\)
0.981075 + 0.193629i \(0.0620258\pi\)
\(410\) 0 0
\(411\) 128.537 + 310.315i 0.312742 + 0.755025i
\(412\) 0 0
\(413\) 29.5039 71.2287i 0.0714380 0.172467i
\(414\) 0 0
\(415\) 130.198i 0.313730i
\(416\) 0 0
\(417\) −118.179 −0.283403
\(418\) 0 0
\(419\) −13.9903 5.79496i −0.0333896 0.0138304i 0.365926 0.930644i \(-0.380752\pi\)
−0.399316 + 0.916813i \(0.630752\pi\)
\(420\) 0 0
\(421\) −507.883 + 210.372i −1.20637 + 0.499696i −0.893053 0.449952i \(-0.851441\pi\)
−0.313320 + 0.949648i \(0.601441\pi\)
\(422\) 0 0
\(423\) 266.790 + 266.790i 0.630708 + 0.630708i
\(424\) 0 0
\(425\) 83.4900 + 83.4900i 0.196447 + 0.196447i
\(426\) 0 0
\(427\) −189.833 + 78.6313i −0.444573 + 0.184148i
\(428\) 0 0
\(429\) −12.0025 4.97159i −0.0279778 0.0115888i
\(430\) 0 0
\(431\) −654.734 −1.51910 −0.759552 0.650447i \(-0.774582\pi\)
−0.759552 + 0.650447i \(0.774582\pi\)
\(432\) 0 0
\(433\) 366.488i 0.846392i −0.906038 0.423196i \(-0.860908\pi\)
0.906038 0.423196i \(-0.139092\pi\)
\(434\) 0 0
\(435\) 139.660 337.170i 0.321058 0.775103i
\(436\) 0 0
\(437\) 7.95524 + 19.2057i 0.0182042 + 0.0439489i
\(438\) 0 0
\(439\) −124.489 + 124.489i −0.283573 + 0.283573i −0.834532 0.550959i \(-0.814262\pi\)
0.550959 + 0.834532i \(0.314262\pi\)
\(440\) 0 0
\(441\) −77.5759 + 77.5759i −0.175909 + 0.175909i
\(442\) 0 0
\(443\) −147.480 356.047i −0.332911 0.803718i −0.998359 0.0572735i \(-0.981759\pi\)
0.665448 0.746445i \(-0.268241\pi\)
\(444\) 0 0
\(445\) −14.5322 + 35.0839i −0.0326567 + 0.0788402i
\(446\) 0 0
\(447\) 185.186i 0.414286i
\(448\) 0 0
\(449\) −689.326 −1.53525 −0.767623 0.640901i \(-0.778561\pi\)
−0.767623 + 0.640901i \(0.778561\pi\)
\(450\) 0 0
\(451\) 784.465 + 324.936i 1.73939 + 0.720479i
\(452\) 0 0
\(453\) 355.788 147.372i 0.785403 0.325325i
\(454\) 0 0
\(455\) −8.77817 8.77817i −0.0192927 0.0192927i
\(456\) 0 0
\(457\) 86.4503 + 86.4503i 0.189169 + 0.189169i 0.795337 0.606168i \(-0.207294\pi\)
−0.606168 + 0.795337i \(0.707294\pi\)
\(458\) 0 0
\(459\) 633.181 262.272i 1.37948 0.571399i
\(460\) 0 0
\(461\) −3.31579 1.37344i −0.00719259 0.00297927i 0.379084 0.925362i \(-0.376239\pi\)
−0.386277 + 0.922383i \(0.626239\pi\)
\(462\) 0 0
\(463\) −113.007 −0.244075 −0.122038 0.992525i \(-0.538943\pi\)
−0.122038 + 0.992525i \(0.538943\pi\)
\(464\) 0 0
\(465\) 308.072i 0.662521i
\(466\) 0 0
\(467\) 150.402 363.102i 0.322059 0.777520i −0.677075 0.735914i \(-0.736753\pi\)
0.999134 0.0416055i \(-0.0132473\pi\)
\(468\) 0 0
\(469\) 60.1753 + 145.276i 0.128306 + 0.309757i
\(470\) 0 0
\(471\) −99.9053 + 99.9053i −0.212113 + 0.212113i
\(472\) 0 0
\(473\) 168.522 168.522i 0.356282 0.356282i
\(474\) 0 0
\(475\) 32.2275 + 77.8040i 0.0678473 + 0.163798i
\(476\) 0 0
\(477\) 69.7759 168.454i 0.146281 0.353153i
\(478\) 0 0
\(479\) 205.624i 0.429278i 0.976693 + 0.214639i \(0.0688575\pi\)
−0.976693 + 0.214639i \(0.931142\pi\)
\(480\) 0 0
\(481\) 19.4390 0.0404136
\(482\) 0 0
\(483\) −9.65155 3.99780i −0.0199825 0.00827702i
\(484\) 0 0
\(485\) 280.302 116.105i 0.577942 0.239391i
\(486\) 0 0
\(487\) −573.249 573.249i −1.17710 1.17710i −0.980479 0.196623i \(-0.937002\pi\)
−0.196623 0.980479i \(-0.562998\pi\)
\(488\) 0 0
\(489\) −252.477 252.477i −0.516313 0.516313i
\(490\) 0 0
\(491\) −421.115 + 174.432i −0.857669 + 0.355258i −0.767795 0.640695i \(-0.778646\pi\)
−0.0898735 + 0.995953i \(0.528646\pi\)
\(492\) 0 0
\(493\) 1153.74 + 477.897i 2.34025 + 0.969364i
\(494\) 0 0
\(495\) −423.914 −0.856392
\(496\) 0 0
\(497\) 139.867i 0.281423i
\(498\) 0 0
\(499\) −115.301 + 278.361i −0.231064 + 0.557837i −0.996303 0.0859086i \(-0.972621\pi\)
0.765239 + 0.643746i \(0.222621\pi\)
\(500\) 0 0
\(501\) 71.1147 + 171.686i 0.141946 + 0.342687i
\(502\) 0 0
\(503\) −526.474 + 526.474i −1.04667 + 1.04667i −0.0478110 + 0.998856i \(0.515225\pi\)
−0.998856 + 0.0478110i \(0.984775\pi\)
\(504\) 0 0
\(505\) 81.0930 81.0930i 0.160580 0.160580i
\(506\) 0 0
\(507\) 110.578 + 266.958i 0.218102 + 0.526545i
\(508\) 0 0
\(509\) −98.1719 + 237.008i −0.192872 + 0.465634i −0.990500 0.137516i \(-0.956088\pi\)
0.797628 + 0.603150i \(0.206088\pi\)
\(510\) 0 0
\(511\) 100.905i 0.197465i
\(512\) 0 0
\(513\) 488.821 0.952867
\(514\) 0 0
\(515\) 92.0858 + 38.1432i 0.178807 + 0.0740644i
\(516\) 0 0
\(517\) −885.103 + 366.622i −1.71200 + 0.709133i
\(518\) 0 0
\(519\) −60.2895 60.2895i −0.116165 0.116165i
\(520\) 0 0
\(521\) −42.3980 42.3980i −0.0813781 0.0813781i 0.665246 0.746624i \(-0.268327\pi\)
−0.746624 + 0.665246i \(0.768327\pi\)
\(522\) 0 0
\(523\) −160.929 + 66.6589i −0.307703 + 0.127455i −0.531192 0.847252i \(-0.678256\pi\)
0.223488 + 0.974707i \(0.428256\pi\)
\(524\) 0 0
\(525\) −39.0993 16.1955i −0.0744749 0.0308485i
\(526\) 0 0
\(527\) 1054.18 2.00034
\(528\) 0 0
\(529\) 527.796i 0.997724i
\(530\) 0 0
\(531\) 32.1971 77.7306i 0.0606348 0.146385i
\(532\) 0 0
\(533\) 10.3843 + 25.0698i 0.0194827 + 0.0470353i
\(534\) 0 0
\(535\) −371.497 + 371.497i −0.694386 + 0.694386i
\(536\) 0 0
\(537\) −93.2687 + 93.2687i −0.173685 + 0.173685i
\(538\) 0 0
\(539\) −106.605 257.366i −0.197782 0.477488i
\(540\) 0 0
\(541\) −29.6178 + 71.5038i −0.0547465 + 0.132170i −0.948886 0.315618i \(-0.897788\pi\)
0.894140 + 0.447788i \(0.147788\pi\)
\(542\) 0 0
\(543\) 209.121i 0.385121i
\(544\) 0 0
\(545\) 403.937 0.741169
\(546\) 0 0
\(547\) −157.659 65.3046i −0.288225 0.119387i 0.233886 0.972264i \(-0.424856\pi\)
−0.522112 + 0.852877i \(0.674856\pi\)
\(548\) 0 0
\(549\) −207.161 + 85.8089i −0.377342 + 0.156300i
\(550\) 0 0
\(551\) 629.819 + 629.819i 1.14305 + 1.14305i
\(552\) 0 0
\(553\) −566.819 566.819i −1.02499 1.02499i
\(554\) 0 0
\(555\) −283.125 + 117.274i −0.510136 + 0.211305i
\(556\) 0 0
\(557\) −890.709 368.944i −1.59912 0.662376i −0.607827 0.794069i \(-0.707959\pi\)
−0.991291 + 0.131693i \(0.957959\pi\)
\(558\) 0 0
\(559\) 7.61638 0.0136250
\(560\) 0 0
\(561\) 700.821i 1.24923i
\(562\) 0 0
\(563\) −106.191 + 256.369i −0.188617 + 0.455362i −0.989694 0.143200i \(-0.954261\pi\)
0.801077 + 0.598562i \(0.204261\pi\)
\(564\) 0 0
\(565\) 17.2037 + 41.5333i 0.0304490 + 0.0735103i
\(566\) 0 0
\(567\) 41.0398 41.0398i 0.0723806 0.0723806i
\(568\) 0 0
\(569\) −351.714 + 351.714i −0.618126 + 0.618126i −0.945050 0.326925i \(-0.893988\pi\)
0.326925 + 0.945050i \(0.393988\pi\)
\(570\) 0 0
\(571\) −179.708 433.854i −0.314725 0.759814i −0.999517 0.0310755i \(-0.990107\pi\)
0.684792 0.728739i \(-0.259893\pi\)
\(572\) 0 0
\(573\) 148.987 359.688i 0.260013 0.627727i
\(574\) 0 0
\(575\) 4.87703i 0.00848179i
\(576\) 0 0
\(577\) 662.602 1.14836 0.574179 0.818730i \(-0.305321\pi\)
0.574179 + 0.818730i \(0.305321\pi\)
\(578\) 0 0
\(579\) 73.4898 + 30.4405i 0.126925 + 0.0525742i
\(580\) 0 0
\(581\) −147.532 + 61.1096i −0.253927 + 0.105180i
\(582\) 0 0
\(583\) 327.375 + 327.375i 0.561535 + 0.561535i
\(584\) 0 0
\(585\) −9.57946 9.57946i −0.0163751 0.0163751i
\(586\) 0 0
\(587\) −650.448 + 269.424i −1.10809 + 0.458985i −0.860279 0.509824i \(-0.829711\pi\)
−0.247809 + 0.968809i \(0.579711\pi\)
\(588\) 0 0
\(589\) 694.650 + 287.733i 1.17937 + 0.488512i
\(590\) 0 0
\(591\) 345.625 0.584814
\(592\) 0 0
\(593\) 430.692i 0.726293i 0.931732 + 0.363147i \(0.118298\pi\)
−0.931732 + 0.363147i \(0.881702\pi\)
\(594\) 0 0
\(595\) −256.277 + 618.708i −0.430718 + 1.03985i
\(596\) 0 0
\(597\) 50.5082 + 121.938i 0.0846033 + 0.204250i
\(598\) 0 0
\(599\) 16.0528 16.0528i 0.0267993 0.0267993i −0.693580 0.720379i \(-0.743968\pi\)
0.720379 + 0.693580i \(0.243968\pi\)
\(600\) 0 0
\(601\) 201.233 201.233i 0.334831 0.334831i −0.519587 0.854418i \(-0.673914\pi\)
0.854418 + 0.519587i \(0.173914\pi\)
\(602\) 0 0
\(603\) 65.6682 + 158.537i 0.108902 + 0.262914i
\(604\) 0 0
\(605\) 201.984 487.633i 0.333858 0.806005i
\(606\) 0 0
\(607\) 713.329i 1.17517i −0.809162 0.587586i \(-0.800079\pi\)
0.809162 0.587586i \(-0.199921\pi\)
\(608\) 0 0
\(609\) −447.609 −0.734990
\(610\) 0 0
\(611\) −28.2860 11.7164i −0.0462946 0.0191759i
\(612\) 0 0
\(613\) −349.658 + 144.833i −0.570404 + 0.236269i −0.649195 0.760622i \(-0.724894\pi\)
0.0787907 + 0.996891i \(0.474894\pi\)
\(614\) 0 0
\(615\) −302.490 302.490i −0.491854 0.491854i
\(616\) 0 0
\(617\) 185.331 + 185.331i 0.300374 + 0.300374i 0.841160 0.540786i \(-0.181873\pi\)
−0.540786 + 0.841160i \(0.681873\pi\)
\(618\) 0 0
\(619\) 740.280 306.634i 1.19593 0.495370i 0.306248 0.951952i \(-0.400926\pi\)
0.889681 + 0.456582i \(0.150926\pi\)
\(620\) 0 0
\(621\) −26.1538 10.8332i −0.0421156 0.0174448i
\(622\) 0 0
\(623\) 46.5755 0.0747601
\(624\) 0 0
\(625\) 494.120i 0.790591i
\(626\) 0 0
\(627\) −191.286 + 461.805i −0.305081 + 0.736532i
\(628\) 0 0
\(629\) −401.295 968.812i −0.637989 1.54024i
\(630\) 0 0
\(631\) −25.0415 + 25.0415i −0.0396854 + 0.0396854i −0.726671 0.686986i \(-0.758934\pi\)
0.686986 + 0.726671i \(0.258934\pi\)
\(632\) 0 0
\(633\) 110.919 110.919i 0.175227 0.175227i
\(634\) 0 0
\(635\) −103.075 248.845i −0.162323 0.391882i
\(636\) 0 0
\(637\) 3.40686 8.22488i 0.00534828 0.0129119i
\(638\) 0 0
\(639\) 152.634i 0.238864i
\(640\) 0 0
\(641\) −150.813 −0.235278 −0.117639 0.993056i \(-0.537533\pi\)
−0.117639 + 0.993056i \(0.537533\pi\)
\(642\) 0 0
\(643\) 635.355 + 263.173i 0.988110 + 0.409289i 0.817424 0.576037i \(-0.195402\pi\)
0.170686 + 0.985325i \(0.445402\pi\)
\(644\) 0 0
\(645\) −110.931 + 45.9492i −0.171987 + 0.0712391i
\(646\) 0 0
\(647\) 460.454 + 460.454i 0.711675 + 0.711675i 0.966885 0.255211i \(-0.0821448\pi\)
−0.255211 + 0.966885i \(0.582145\pi\)
\(648\) 0 0
\(649\) 151.062 + 151.062i 0.232762 + 0.232762i
\(650\) 0 0
\(651\) −349.087 + 144.597i −0.536232 + 0.222115i
\(652\) 0 0
\(653\) 308.661 + 127.852i 0.472682 + 0.195791i 0.606291 0.795243i \(-0.292657\pi\)
−0.133609 + 0.991034i \(0.542657\pi\)
\(654\) 0 0
\(655\) 865.779 1.32180
\(656\) 0 0
\(657\) 110.115i 0.167603i
\(658\) 0 0
\(659\) 187.311 452.209i 0.284235 0.686205i −0.715690 0.698418i \(-0.753888\pi\)
0.999925 + 0.0122131i \(0.00388764\pi\)
\(660\) 0 0
\(661\) −279.659 675.156i −0.423084 1.02142i −0.981432 0.191809i \(-0.938564\pi\)
0.558348 0.829607i \(-0.311436\pi\)
\(662\) 0 0
\(663\) −15.8369 + 15.8369i −0.0238867 + 0.0238867i
\(664\) 0 0
\(665\) −337.747 + 337.747i −0.507891 + 0.507891i
\(666\) 0 0
\(667\) −19.7397 47.6558i −0.0295947 0.0714479i
\(668\) 0 0
\(669\) −280.535 + 677.271i −0.419335 + 1.01236i
\(670\) 0 0
\(671\) 569.360i 0.848525i
\(672\) 0 0
\(673\) 74.6107 0.110863 0.0554314 0.998462i \(-0.482347\pi\)
0.0554314 + 0.998462i \(0.482347\pi\)
\(674\) 0 0
\(675\) −105.951 43.8865i −0.156965 0.0650170i
\(676\) 0 0
\(677\) −250.770 + 103.872i −0.370413 + 0.153430i −0.560122 0.828410i \(-0.689246\pi\)
0.189709 + 0.981840i \(0.439246\pi\)
\(678\) 0 0
\(679\) −263.124 263.124i −0.387517 0.387517i
\(680\) 0 0
\(681\) −147.031 147.031i −0.215905 0.215905i
\(682\) 0 0
\(683\) −1198.32 + 496.359i −1.75449 + 0.726734i −0.757200 + 0.653183i \(0.773433\pi\)
−0.997291 + 0.0735510i \(0.976567\pi\)
\(684\) 0 0
\(685\) −821.671 340.347i −1.19952 0.496857i
\(686\) 0 0
\(687\) −237.286 −0.345395
\(688\) 0 0
\(689\) 14.7958i 0.0214743i
\(690\) 0 0
\(691\) 337.819 815.567i 0.488884 1.18027i −0.466398 0.884575i \(-0.654449\pi\)
0.955282 0.295696i \(-0.0955514\pi\)
\(692\) 0 0
\(693\) 198.968 + 480.351i 0.287111 + 0.693147i
\(694\) 0 0
\(695\) 221.269 221.269i 0.318372 0.318372i
\(696\) 0 0
\(697\) 1035.08 1035.08i 1.48504 1.48504i
\(698\) 0 0
\(699\) 83.9591 + 202.695i 0.120113 + 0.289979i
\(700\) 0 0
\(701\) 487.432 1176.77i 0.695338 1.67870i −0.0383989 0.999262i \(-0.512226\pi\)
0.733737 0.679433i \(-0.237774\pi\)
\(702\) 0 0
\(703\) 747.930i 1.06391i
\(704\) 0 0
\(705\) 482.666 0.684632
\(706\) 0 0
\(707\) −129.951 53.8274i −0.183806 0.0761349i
\(708\) 0 0
\(709\) 949.384 393.248i 1.33905 0.554651i 0.405824 0.913951i \(-0.366985\pi\)
0.933222 + 0.359300i \(0.116985\pi\)
\(710\) 0 0
\(711\) −618.559 618.559i −0.869985 0.869985i
\(712\) 0 0
\(713\) −30.7896 30.7896i −0.0431832 0.0431832i
\(714\) 0 0
\(715\) 31.7809 13.1641i 0.0444487 0.0184113i
\(716\) 0 0
\(717\) 448.906 + 185.943i 0.626089 + 0.259335i
\(718\) 0 0
\(719\) −349.072 −0.485496 −0.242748 0.970089i \(-0.578049\pi\)
−0.242748 + 0.970089i \(0.578049\pi\)
\(720\) 0 0
\(721\) 122.248i 0.169554i
\(722\) 0 0
\(723\) 202.788 489.573i 0.280481 0.677141i
\(724\) 0 0
\(725\) −79.9673 193.058i −0.110300 0.266287i
\(726\) 0 0
\(727\) 256.931 256.931i 0.353413 0.353413i −0.507965 0.861378i \(-0.669602\pi\)
0.861378 + 0.507965i \(0.169602\pi\)
\(728\) 0 0
\(729\) −236.352 + 236.352i −0.324214 + 0.324214i
\(730\) 0 0
\(731\) −157.231 379.590i −0.215091 0.519275i
\(732\) 0 0
\(733\) 473.293 1142.63i 0.645694 1.55884i −0.173194 0.984888i \(-0.555409\pi\)
0.818887 0.573955i \(-0.194591\pi\)
\(734\) 0 0
\(735\) 140.347i 0.190949i
\(736\) 0 0
\(737\) −435.722 −0.591211
\(738\) 0 0
\(739\) 137.009 + 56.7511i 0.185398 + 0.0767945i 0.473451 0.880820i \(-0.343008\pi\)
−0.288053 + 0.957614i \(0.593008\pi\)
\(740\) 0 0
\(741\) −14.7583 + 6.11310i −0.0199168 + 0.00824979i
\(742\) 0 0
\(743\) 644.593 + 644.593i 0.867555 + 0.867555i 0.992201 0.124647i \(-0.0397797\pi\)
−0.124647 + 0.992201i \(0.539780\pi\)
\(744\) 0 0
\(745\) 346.727 + 346.727i 0.465405 + 0.465405i
\(746\) 0 0
\(747\) −160.999 + 66.6878i −0.215527 + 0.0892742i
\(748\) 0 0
\(749\) 595.321 + 246.590i 0.794821 + 0.329225i
\(750\) 0 0
\(751\) 18.5402 0.0246873 0.0123437 0.999924i \(-0.496071\pi\)
0.0123437 + 0.999924i \(0.496071\pi\)
\(752\) 0 0
\(753\) 151.836i 0.201641i
\(754\) 0 0
\(755\) −390.220 + 942.075i −0.516848 + 1.24778i
\(756\) 0 0
\(757\) 100.854 + 243.482i 0.133228 + 0.321641i 0.976389 0.216021i \(-0.0693079\pi\)
−0.843161 + 0.537661i \(0.819308\pi\)
\(758\) 0 0
\(759\) 20.4691 20.4691i 0.0269685 0.0269685i
\(760\) 0 0
\(761\) −272.267 + 272.267i −0.357775 + 0.357775i −0.862992 0.505217i \(-0.831412\pi\)
0.505217 + 0.862992i \(0.331412\pi\)
\(762\) 0 0
\(763\) −189.591 457.714i −0.248482 0.599888i
\(764\) 0 0
\(765\) −279.671 + 675.185i −0.365583 + 0.882594i
\(766\) 0 0
\(767\) 6.82730i 0.00890130i
\(768\) 0 0
\(769\) −341.927 −0.444638 −0.222319 0.974974i \(-0.571363\pi\)
−0.222319 + 0.974974i \(0.571363\pi\)
\(770\) 0 0
\(771\) −305.417 126.508i −0.396131 0.164083i
\(772\) 0 0
\(773\) −366.728 + 151.904i −0.474421 + 0.196512i −0.607065 0.794652i \(-0.707653\pi\)
0.132644 + 0.991164i \(0.457653\pi\)
\(774\) 0 0
\(775\) −124.732 124.732i −0.160944 0.160944i
\(776\) 0 0
\(777\) 265.775 + 265.775i 0.342053 + 0.342053i
\(778\) 0 0
\(779\) 964.582 399.543i 1.23823 0.512892i
\(780\) 0 0
\(781\) −358.065 148.315i −0.458470 0.189904i
\(782\) 0 0
\(783\) −1212.93 −1.54908
\(784\) 0 0
\(785\) 374.109i 0.476572i
\(786\) 0 0
\(787\) −167.684 + 404.824i −0.213067 + 0.514389i −0.993892 0.110361i \(-0.964799\pi\)
0.780825 + 0.624750i \(0.214799\pi\)
\(788\) 0 0
\(789\) −13.4179 32.3938i −0.0170063 0.0410568i
\(790\) 0 0
\(791\) 38.9881 38.9881i 0.0492896 0.0492896i
\(792\) 0 0
\(793\) 12.8662 12.8662i 0.0162247 0.0162247i
\(794\) 0 0
\(795\) −89.2623 215.498i −0.112280 0.271067i
\(796\) 0 0
\(797\) −230.548 + 556.591i −0.289269 + 0.698358i −0.999987 0.00511971i